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# Susan has a 5-foot long bookshelf that she wants to fill

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Manager
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Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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07 Jun 2011, 15:46
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95% (hard)

Question Stats:

38% (02:15) correct 62% (01:41) wrong based on 254 sessions

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Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf?

(1) The 8 thinnest books each have a thickness of 2 inches.

(2) The 2 thickest books each have a thickness of 5 inches.
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07 Jun 2011, 20:59
st-1 ==> not sufficient, we definitely the size of thickest book(s). Alternatively, we have smallest size book from which we can determine what space of the shelf is utilized. Now for the remaining space, you can assume like the book is 1 ft thick and very few books will be filled or the book is just 2.1 inches thick... so doesnt help much.

St-2 ==> 22 books require 5.5 ft i.e. 65 inches.

2 books utilized 5 inch each. so remaining 20 books are left with 55 inches.
or approximately 2.75" each book.

we know that 22 books cannot fit in 5 ft but needs 5.5 ft.
so from above we can conclude that (approx.) 2 books are not able to fit and that is why additional 0.5 ft is required.

And in 5 ft shelf, only 20 books can fit.

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07 Jun 2011, 21:23
agdimple333, could you please explain this line ?

so from above we can conclude that (approx.) 2 books are not able to fit and that is why additional 0.5 ft is required.
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08 Jun 2011, 07:18
subhashghosh wrote:
agdimple333, could you please explain this line ?

so from above we can conclude that (approx.) 2 books are not able to fit and that is why additional 0.5 ft is required.

0.5 ft = 6" and it was concluded that approx size of each book is 2.75", so in that extra space of 6" approx we are fitting 2 books.

Its a DS Q, so an estimation is better & saves time than actually deriving the exact #s.

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08 Jun 2011, 10:02
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smodak wrote:
Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf?

(1) The 8 thinnest books each have a thickness of 2 inches.

(2) The 2 thickest books each have a thickness of 5 inches.

65 inch can accommodate all the books. But have to find the max number of books that can be accomodated in 5 foot long bookshelf.
This could be done by avoiding the thickest books.
If you avoid one 5inch thickest book.
Number of books = 22-1 = 21
total thickness = 65-5 = 60 = 5 feet

Hence 21 books can be accommodated. Sufficient.

Hence B
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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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02 Oct 2014, 00:37
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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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28 Oct 2014, 03:13
Might be a stupid question, but are we supposed to know these conversions, i.e. foot to inch, et al. ?

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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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28 Oct 2014, 03:35
jegan2388 wrote:
Might be a stupid question, but are we supposed to know these conversions, i.e. foot to inch, et al. ?

No. The question itself will supply the relative conversions. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ...

Check other Conversion problems to practice in Special Questions Directory.
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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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23 Nov 2014, 22:36
5.5 foot is 66 inches right? not sure why everyone is referring to 65?
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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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07 Dec 2014, 00:09
Sorry but isn't 5.5=66 inches?
so from B, if you avoid the thickest book of 5 inches, you will have 61 inches, but the shelf is only 60 inches long...should you drop the second 5" book as well?

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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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07 Dec 2014, 05:47
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usre123 wrote:
Sorry but isn't 5.5=66 inches?
so from B, if you avoid the thickest book of 5 inches, you will have 61 inches, but the shelf is only 60 inches long...should you drop the second 5" book as well?

Yes, 5.5 feet is 66 inches and the shelf is only 60 inches long. To maximize the number of books on the shelf, Susan should start removing thickest books. If she removes only one 5-inch book, she'd be left with 61 inch long books, thus she must remove both 5-inch books, which means that Susan can fit maximum of 20 books on her 60-inch shelf.

Hope it's clear.
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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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07 Dec 2014, 11:23
yes, it's clear, thank you!

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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

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12 Sep 2016, 10:18
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Re: Susan has a 5-foot long bookshelf that she wants to fill   [#permalink] 12 Sep 2016, 10:18
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# Susan has a 5-foot long bookshelf that she wants to fill

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